Finite Group Databasebeta

← C2×#13073786 #14925696

Subgroups — C2×#13073786 #14925696

Order 2816.

3222 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D11C211yesmaximal, characteristic
3#13073786C2116yesmaximal, direct product factor
4C2×#10622286C212yesmaximal, complemented
5C2×#10622560C212yesmaximal, complemented
6C2×#10622570C212yesmaximal
7C2×#10622263C212yesmaximal, complemented
8C2×#10622825C211yesmaximal, characteristic, complemented
9C2×#10622600C211yesmaximal, characteristic, complemented
10C2×#10622600C211yesmaximal, characteristic, complemented
11C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
12C2×C11×#380C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C23×Dic22C2212yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C2×C4×C22⋊D11—28no—
23C2×C4×C22⋊D11C2218yes—
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2212yes—
30C22×Dic11⋊C4C2211yescharacteristic
31C22×C4×Dic11C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C2×#66941—28no—
34C2×#66941C2218yescomplemented
35C11×#380C2218yescomplemented
36C2×C11×#95C2212yes—
37#10622825C2218yescomplemented
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622600C2218yescomplemented
43#10622600C2218yescomplemented
44C4⋊C4×Dic11C2218yescomplemented
45#10622570C22116yes—
46#10622560C22116yescomplemented
47#10622286C22116yescomplemented
48#10622263C22116yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C23×C4×C11—24no—
52C23×C4×C11—24no—
53C23×C4×C11—24no—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2312yes—
57C23×C4×C11C2314yes—
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—24no—
60C22×C22⋊D11—24no—
61C22×C22⋊D11Q818yescomplemented
62C22×C22⋊D11C2314yes—
63C23×Dic11C2312yes—
64C23×Dic11C2312yes—
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C22×C4×D11—24no—
69C22×C4×D11—24no—
70C22×C4×D11—24no—
71C22×C4×D11C2314yes—
72C22×Dic22—28no—
73C22×Dic22—44no—
74C22×Dic22—44no—
75C22×Dic22C2318yes—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C22⋊C4—44no—
81C2×C11×C22⋊C4C2318yes—
82C2×C22⋊Dic11—24no—
83C2×C22⋊Dic11—44no—
84C2×C22⋊Dic11C2314yes—
85C2×C22⋊Dic11C2318yes—
86C4×C22⋊D11—232no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—44no—
89C2×(C2×D11)⋊C4—44no—
90C2×(C2×D11)⋊C4C2314yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×C4⋊Dic11—24no—
94C2×C4⋊Dic11—24no—
95C2×C4⋊Dic11C2314yes—
96C2×C4⋊Dic11C2314yes—
97C2×Dic11⋊C4—28no—
98C2×Dic11⋊C4—24no—
99C2×Dic11⋊C4C2318yes—
100C2×Dic11⋊C4C2314yes—
101C2×C4×Dic11—28no—
102C2×C4×Dic11D418yes—
103C2×C4×Dic11C2318yes—
104C2×C4×Dic11C2314yes—
105#66941—232no—
106C11×#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C2×#2563—111nomaximal, Sylow
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11C2×Q814yes—
119C24×C11C2412yes—
120C24×C11C2411yescharacteristic
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—22no—
126C23×D11—22no—
127C23×D11C2×Q814yes—
128C23×D11C2412yes—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—28no—
139C22×C4×C11—28no—
140C22×C4×C11—28no—
141C22×C4×C11—416no—
142C22×C4×C11C2×D414yes—
143C22×C4×C11#4114yes—
144C22×C4×C11#4114yes—
145C22×C4×C11C2412yes—
146C22×C4×C11C2414yes—
147C22×C4×C11C2414yes—
148C22×C4×C11C2412yes—
149C2×C22⋊D11—232no—
150C2×C22⋊D11—28no—
151C2×C22⋊D11—28no—
152C2×C22⋊D11C2×Q8116yescomplemented
153C22×Dic11—24no—
154C22×Dic11—22no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11C2×D414yes—
165C22×Dic11C2×D414yes—
166C22×Dic11C2×Q814yes—
167C22×Dic11#4114yes—
168C22×Dic11C2412yes—
169C22×Dic11C2414yes—
170C22×Dic11C2414yes—
171C22×Dic11C2412yes—
172C22×Dic11C2412yes—
173C2×C4×D11—28no—
174C2×C4×D11—28no—
175C2×C4×D11—28no—
176C2×C4×D11—416no—
177C2×Dic22—216no—
178C2×Dic22—48no—
179C2×Dic22—48no—
180C2×Dic22—432no—
181C11×C4⋊C4—28no—
182C11×C4⋊C4—28no—
183C11×C22⋊C4—48no—
184C22⋊Dic11—28no—
185C22⋊Dic11—48no—
186(C2×D11)⋊C4—28no—
187(C2×D11)⋊C4—48no—
188(C2×D11)⋊C4—48no—
189C4⋊Dic11—28no—
190C4⋊Dic11—28no—
191Dic11⋊C4—216no—
192Dic11⋊C4—28no—
193C4×Dic11—216no—
194C4×Dic11C2×D4116yes—
195C22×C4⋊Q8—111no—
196C22×C4×D4—111no—
197#2563—1116no—
198C2×#393—112no—
199C2×#393—112no—
200C2×#390—112no—
201C2×#382—112no—
202C2×#380—111no—
203C2×#380—111no—
204C2×#380—111no—
205C2×#380D1111yescharacteristic, complemented
206C2×C4×C4⋊C4—111no—
207C23×C11—28no—
208C23×C11—28no—
209C23×C11—28no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—44no—
217C23×C11—44no—
218C23×C11—44no—
219C23×C11—44no—
220C23×C11C22×D412yes—
221C23×C11C22×Q814yes—
222C23×C11C22×Q812yes—
223C23×C11C2×#4112yes—
224C23×C11C2×#4112yes—
225C23×C11C2×#4112yes—
226C23×C11H(5,𝔽2)12yes—
227C23×C11H(5,𝔽2)12yes—
228C23×C11C2511yescharacteristic
229C22×D11—28no—
230C22×D11—28no—
231C22×D11—28no—
232C22×D11—22no—
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—22no—
238C22×D11—44no—
239C22×D11—44no—
240C22×D11—44no—
241C22×D11—44no—
242C22×D11C22×Q814yes—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—44no—
253C2×C4×C11—48no—
254C2×C4×C11—48no—
255C2×C4×C11—416no—
256C2×C4×C11#124116yes—
257C2×C4×C11C22×D414yes—
258C2×C4×C11C2×#4114yes—
259C2×C4×C11C2×#4114yes—
260C22⋊D11—232no—
261C2×Dic11—28no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—44no—
274C2×Dic11—48no—
275C2×Dic11—48no—
276C2×Dic11C22⋊Q8116yes—
277C2×Dic11C22×D414yes—
278C2×Dic11C22×D414yes—
279C2×Dic11C22×Q814yes—
280C2×Dic11C2×#4114yes—
281C4×D11—416no—
282Dic22—432no—
283C23×Q8—112no—
284C23×D4—111no—
285C24×C4—111no—
286C24×C4C2×D1111yescharacteristic
287C2×C4⋊Q8—118no—
288C2×C4⋊Q8—228no—
289C2×C4×D4—118no—
290C2×C4×D4—228no—
291C22×C4⋊C4—111no—
292C22×C4⋊C4—112no—
293C22×C4⋊C4—111no—
294C22×C4⋊C4—111no—
295C22×C4⋊C4C2×D1111yescharacteristic
296C22×C4⋊C4C2×D1111yescharacteristic
297C22×C22⋊C4—111no—
298C22×C22⋊C4—111no—
299C22×C22⋊C4—112no—
300C22×C22⋊C4—112no—
301C22×C22⋊C4—112no—
302C22×C22⋊C4C2×D1112yes—
303C22×C42—111no—
304C22×C42—112no—
305#393—1116no—
306#393—1116no—
307#390—1116no—
308#382—1116no—
309#380—118no—
310#380—118no—
311#380—118no—
312#380C2×D1118yescomplemented
313C4×C4⋊C4—118no—
314C2×#95—112no—
315C2×#95—112no—
316C2×#95—112no—
317C2×#95—112no—
318C2×#95C2×D1112yes—
319C22×C11—24no—
320C22×C11—24no—
321C22×C11—24no—
322C22×C11—416no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11C2×C22⋊Q814yes—
328C22×C11C2×#12414yes—
329C22×C11#53514yes—
330C22×C11#55414yes—
331C22×C11#55414yes—
332C22×C11#55514yes—
333C22×C11#55514yes—
334C22×C11C23×D411yescharacteristic
335C22×C11C23×Q811yescharacteristic
336C22×C11C22×#4111yescharacteristic
337C22×C11C22×#4111yescharacteristic
338C22×C11C22×#4111yescharacteristic
339C22×C11C2×H(5,𝔽2)11yescharacteristic
340C22×C11C2×H(5,𝔽2)11yescharacteristic
341C2×D11—24no—
342C2×D11—24no—
343C2×D11—24no—
344C2×D11—416no—
345C2×D11—42no—
346C2×D11—42no—
347C2×D11—42no—
348C2×D11—42no—
349C4×C11—42no—
350C4×C11—44no—
351C4×C11—44no—
352C4×C11C2×#12418yes—
353Dic11—24no—
354Dic11—42no—
355Dic11—44no—
356Dic11—44no—
357Dic11C2×C22⋊Q818yes—
358C25—111no—
359C25C22×D1111yescharacteristic
360C22×Q8—118no—
361C22×Q8—228no—
362C22×Q8—444no—
363C22×Q8—444no—
364C22×D4—118no—
365C22×D4—114no—
366C22×D4—224no—
367C22×D4—224no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—111no—
372C23×C4—111no—
373C23×C4—112no—
374C23×C4—112no—
375C23×C4—111no—
376C23×C4—114no—
377C23×C4—224no—
378C23×C4—224no—
379C23×C4—224no—
380C23×C4C22×D1114yes—
381C23×C4C22×D1112yes—
382C23×C4C22×D1112yes—
383C23×C4C22×D1111yescharacteristic
384C23×C4C22×D1111yescharacteristic
385C4⋊Q8—2232no—
386C4×D4—2232no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—114no—
390C2×C4⋊C4—114no—
391C2×C4⋊C4—118no—
392C2×C4⋊C4—114no—
393C2×C4⋊C4—224no—
394C2×C4⋊C4—228no—
395C2×C4⋊C4—224no—
396C2×C4⋊C4—224no—
397C2×C4⋊C4C22×D1114yes—
398C2×C4⋊C4C22×D1114yes—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—114no—
401C2×C22⋊C4—114no—
402C2×C22⋊C4—118no—
403C2×C22⋊C4—118no—
404C2×C22⋊C4—118no—
405C2×C22⋊C4—224no—
406C2×C22⋊C4—224no—
407C2×C22⋊C4—444no—
408C2×C22⋊C4—444no—
409C2×C22⋊C4—444no—
410C2×C22⋊C4C22×D1118yes—
411C2×C42—118no—
412C2×C42—114no—
413C2×C42—118no—
414C2×C42—228no—
415#95—118no—
416#95—118no—
417#95—118no—
418#95—118no—
419#95C22×D1118yes—
420C2×C11—44no—
421C2×C11#256318yescomplemented
422C2×C11C22×C22⋊Q811yescharacteristic
423C2×C11C22×#12411yescharacteristic
424C2×C11C2×#53511yescharacteristic
425C2×C11C2×#55411yescharacteristic
426C2×C11C2×#55411yescharacteristic
427C2×C11C2×#55511yescharacteristic
428C2×C11C2×#55511yescharacteristic
429D11—44no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—114no—
437C24—112no—
438C24—222no—
439C24—222no—
440C24—222no—
441C24—222no—
442C24—222no—
443C24—222no—
444C24Q8×D1114yes—
445C24C23×D1112yes—
446C24C23×D1111yescharacteristic
447C2×Q8—2216no—
448C2×Q8—448no—
449C2×Q8—448no—
450C2×Q8—4432no—
451C2×D4—1116no—
452C2×D4—228no—
453C2×D4—2232no—
454C2×D4—228no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—416no—
468C22×C4—114no—
469C22×C4—114no—
470C22×C4—114no—
471C22×C4—112no—
472C22×C4—114no—
473C22×C4—112no—
474C22×C4—112no—
475C22×C4—114no—
476C22×C4—114no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—224no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—224no—
483C22×C4—222no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—224no—
487C22×C4—224no—
488C22×C4—228no—
489C22×C4—228no—
490C22×C4—228no—
491C22×C4—4416no—
492C22×C4#433914yes—
493C22×C4D4×D1114yes—
494C22×C4#434114yes—
495C22×C4C23×D1112yes—
496C22×C4C23×D1114yes—
497C22×C4C23×D1114yes—
498C22×C4C23×D1112yes—
499C4⋊C4—28no—
500C4⋊C4—28no—
501C4⋊C4—228no—
502C4⋊C4—2216no—
503C4⋊C4—228no—
504C4⋊C4—228no—
505C22⋊C4—48no—
506C22⋊C4—228no—
507C22⋊C4—228no—
508C22⋊C4—448no—
509C22⋊C4—448no—
510C22⋊C4—448no—
511C42—1116no—
512C42—2216no—
513C11C2×#256311yescharacteristic, complemented, Sylow
514C23—28no—
515C23—28no—
516C23—28no—
517C23—22no—
518C23—22no—
519C23—22no—
520C23—22no—
521C23—22no—
522C23—22no—
523C23—44no—
524C23—44no—
525C23—44no—
526C23—44no—
527C23—114no—
528C23—228no—
529C23—228no—
530C23—228no—
531C23—222no—
532C23—222no—
533C23—222no—
534C23—222no—
535C23—222no—
536C23—222no—
537C23—444no—
538C23—444no—
539C23—444no—
540C23—444no—
541C23C2×#433912yes—
542C23C2×D4×D1112yes—
543C23C2×#434112yes—
544C23#6703712yes—
545C23C2×Q8×D1114yes—
546C23C2×Q8×D1112yes—
547C23#41×D1112yes—
548C23#6704212yes—
549C23C24×D1111yescharacteristic
550Q8—4432no—
551D4—2232no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—44no—
562C2×C4—48no—
563C2×C4—48no—
564C2×C4—416no—
565C2×C4—1116no—
566C2×C4—114no—
567C2×C4—114no—
568C2×C4—114no—
569C2×C4—114no—
570C2×C4—228no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—224no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—224no—
577C2×C4—222no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—444no—
583C2×C4—448no—
584C2×C4—448no—
585C2×C4—4416no—
586C2×C4#66938116yes—
587C2×C4C2×#433914yes—
588C2×C4C2×D4×D1114yes—
589C2×C4C2×#434114yes—
590C22—24no—
591C22—24no—
592C22—24no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22—416no—
598C22—224no—
599C22—224no—
600C22—224no—
601C22—442no—
602C22—442no—
603C22—442no—
604C22—442no—
605C22—4416no—
606C22C2×#6693814yes—
607C22#1062304214yes—
608C22#1062306314yes—
609C22#1062313814yes—
610C22#1062314714yes—
611C22D11×C22⋊Q814yes—
612C22#1062316614yes—
613C22C22×#433911yescharacteristic
614C22C22×D4×D1111yescharacteristic
615C22C22×#434111yescharacteristic
616C22C2×#6703711yescharacteristic
617C22C22×Q8×D1111yescharacteristic
618C22C2×#41×D1111yescharacteristic
619C22C2×#6704211yescharacteristic
620C4—42no—
621C4—44no—
622C4—44no—
623C4—118no—
624C4—224no—
625C4—442no—
626C4—444no—
627C4—444no—
628C4C2×#6693818yes—
629C2—44no—
630C2—444no—
631C2#1307378618yesdirect product factor
632C2C2×D11×C22⋊Q811yescharacteristic
633C2C22×#6693811yescharacteristic
634C2C2×#1062313811yescharacteristic
635C2C2×#1062304211yescharacteristic
636C2C2×#1062316611yescharacteristic
637C2C2×#1062306311yescharacteristic
638C2C2×#1062314711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#380C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#380D11
hypocenterC11C2×#2563
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#66941C2semidirect
3. #13073786C2direct (N × H)
4. C2×#10622286C2semidirect
5. C2×#10622560C2semidirect
7. C2×#10622263C2semidirect
8. C2×#10622825C2semidirect
9. C2×#10622600C2semidirect
10. C2×#10622600C2semidirect
11. C2×C4⋊C4×Dic11C2semidirect
12. C2×C11×#380C2semidirect
34. C2×#66941C22semidirect
35. C11×#380C22semidirect
37. #10622825C22semidirect
42. #10622600C22semidirect
43. #10622600C22semidirect
44. C4⋊C4×Dic11C22semidirect
46. #10622560C22semidirect
47. #10622286C22semidirect
48. #10622263C22semidirect
61. C22×C22⋊D11Q8semidirect
152. C2×C22⋊D11C2×Q8semidirect
205. C2×#380D11semidirect
312. #380C2×D11semidirect
421. C2×C11#2563semidirect
513. C11C2×#2563semidirect
631. C2#13073786direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#669412
C22×C4×C22⋊D112
#130737862
C2×#106222862
C2×#106225602
C2×#106225702
C2×#106222632
C2×#106228252
C2×#106226002
C2×C4⋊C4×Dic112
C2×C11×#3802
C2×#256311